1. IBS Calculation Using BETACOOL He Zhang 2/26/2013 Jlab MEIC R&D Group Meeting

2. He Zhang ---2--- Outline Formulas for IBS rise time IBS rise time calculation using BETACOOL IBS calculation for MEIC&LEIC

3. He Zhang---3--- Formulas for IBS rise time calculation How to derive the formulas? IBS is due to the collisions inside the ion bunch Steps to derive the formulas 1.In beam frame, two body collision, the change of momentum 2.In lab frame, the change of emittance 3.Average over all scattering angles 4.Average over all particles

4. He Zhang---4--- Formulas for IBS rise time calculation

5. He Zhang ---5--- IBS rise time calculation using BETACOOL Set the lattice of the ring Set ring parameters Set beam paramters Choose IBS model Calculate the growth rate How to use BETACOOL:

6. He Zhang---6--- IBS rise time calculation using BETACOOL Set the lattice of the ring Pay attention:

7. He Zhang---7--- IBS rise time calculation using BETACOOL Set ring parameters

8. He Zhang---8--- IBS rise time calculation using BETACOOL Set beam paramters

9. He Zhang---9--- IBS rise time calculation using BETACOOL Choose IBS model BETACOOL manual suggests: Use Martini model with numerical integral over z first. For accuracy<1%, mu, nu, and z need to be a few hundred Then choose “Coulomb logarithm”. Compare the result to find a proper value for Lc. Pay attention: the window value of “Coulomb logarithm” is actually two times “Coulomb logarithm” (2Lc), ~40.

10. He Zhang ---10--- IBS rise time calculation using BETACOOL Calculate the growth rate

11. He Zhang ---11--- IBS rise time calculation using BETACOOL Calculate the growth rate

12. He Zhang ---12--- Discussion about coupling Lijun’s result for MEIC IBS calculation

13. He Zhang ---13--- Discussion about coupling

14. He Zhang ---14--- Discussion about coupling From the physical manual of BETACOOL:

15. He Zhang ---15--- Discussion about coupling From the physical manual of BETACOOL:

16. He Zhang ---16--- IBS calculation for MEIC&LEIC Future work Cooling simualtion Compare different models and formulas Get familiar with other functions of BETACOOL Thanks for your time ! This presentation uses the results from the following persons’ work: A. Piwinski, J. Bjorken, S. Mtingwa, M. Monte, M. Martini, A. Sorensen, F. Zimmermann, J. Wei, G. Parzen, etc.